Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
170 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #28409378 | C2 | semidirect |
| 2. #28409323 | C2 | semidirect |
| 4. #28409109 | C2 | semidirect |
| 5. #28408784 | C2 | semidirect |
| 6. #28408780 | C2 | semidirect |
| 7. #331×C227 | C2 | semidirect |
| 82. C227 | #1697 | semidirect |
| 90. #331 | D227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28409378 | 2 |
| #28409323 | 2 |
| #28409224 | 2 |
| #28409109 | 2 |
| #28408784 | 2 |
| #28408780 | 2 |
| #331×C227 | 2 |
| #1697 | 227 |